Losing charge, even while plugged in.

I'm assuming you have a Nokia gateway since I believe it's the only one with a battery. I believe the sole purpose of the battery is for the initial placement - the battery power allows you to walk around your home with the gateway unplugged to determine the best location (via the bars on the gateway screen). Other than that there's no point to the battery. I think there's discussions on this site regarding just removing it.

I would think if your power adapter was faulty the gateway would be having other problems as well, so more than likely the battery is just losing its ability to hold a charge.

I assume when you say you turn it off at night, you're turning it off by shutting off power to it via a power strip perhaps. If that's the case the battery is obviously not charging overnight, so it's going to drain. The  extreme drop in charge though does tell you the battery is probably dying. Other possibility would be a short somewhere that's causing the drain.

Regardless, the battery doesn't affect the day-to-day operation of the gateway. If it's a concern to you, you can contact T-Mobile and they'll send you a replacement which will likely be a different brand w/o a battery.